n维R球凸体的照明体
Illumination bodies for ball-convex bodies
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中文总结 AI 辅助
在n维R球凸体类中引入照明体和加权照明体，证明其为凸体，表明体积左导数产生相对表面积测度，且在二维中建立了该相对表面积的等周不等式。
中文摘要 AI 辅助
我们在n维R球凸体类中引入了照明体和加权照明体。这些体可被视为最近引入的R球漂浮体的对偶对应物。我们证明了照明体是凸的。我们还表明，体积的左导数产生了球凸体的表面积测度，即相对表面积测度。在二维中，我们建立了这个相对表面积的等周不等式。
英文摘要
We introduce illumination bodies and weighted illumination bodies in the class of $n$-dimensional $R$-ball convex bodies. These bodies may be regarded as dual counterparts of the recently introduced $R$-ball floating bodies. We prove that the illumination bodies are convex. We also show that a left derivative of volume gives rise to a surface area measure for ball-convex bodies, the relative surface area measure. In dimension $2$, we establish an isoperimetric inequality for this relative surface area.
